For a trapezoid, if the upper bottom is reduced by 2.5 cm, it becomes a triangle, and the area is reduced by 8.5 square cm compared with the original trapezoid; if the lower bottom is reduced by 4 cm, It becomes a parallelogram. Find the area of the original trapezoid If you have a series of equations, just X

8.5×2÷2.5
=17÷2.5
=6.8 (CM)
2.5 + 4 = 6.5 (CM)
(2.5+6.5)×6.8÷2
=9×6.8÷2
=30.6 (cm2)
A: the original trapezoid area is 30.6 square centimeters
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Let f (x) = LG (X & sup2; - 2x + a), if a > 1, and the maximum value of F (x) in the interval [- 1,4] is 1, find the value of a?

Let g (x) = x & sup2; - 2x + a = (x-1) & sup2; + A-1 > 0
When x > 1, G (x) increases monotonically,
The maximum value of F (x) on (1,4] is f (4) = LG (a + 8),
When x ＜ 1, G (x) decreases monotonically,
In [- 1,1], the maximum value of F (x) is f (- 1) = LG (a + 3),
And f (1) = LG (A-1),
And LG (A-1) < LG (a + 3) < LG (a + 8), the maximum value of function f (x) in the interval [- 1,4] is 1, so f (4) = LG (a + 8) = 1
So a + 8 = 10, a = 2

The top of the granary is a cone shape. The radius of the bottom of the cone is 3 meters long, and the bus is 6 meters long. In order to prevent water leakage, linoleum needs to be laid on the top of the granary. How much does it cost for 10 yuan per square meter!

Side area of cone = 3.14 × 3 × 6 = 56.52 (M2)
The total price of linoleum is 56.52 × 10 = 565.2 yuan

Given that the intersection of circle x ^ 2 + y ^ 2 = 0 and X axis is a (- 1,0), B (1,0), CD is the moving chord perpendicular to AB, connect CB, ad, find the trajectory equation of intersection of AD and BC

Hello, is the question wrong?
Is the radius of a circle zero?

A triangle and a parallelogram have the same base and height. The area of the parallelogram is 93.2. Find the area of the triangle

A triangle has the same base and height as a parallelogram. The area of a triangle is half that of a parallelogram
The area of the triangle is 93.2 / 2 = 46.6

In 1,2,3 In 2003, there are prime numbers a, composite numbers B, odd numbers C and even numbers D. what is (A-C) + (B-D)?

Except for 1
Other numbers are either prime numbers or composite numbers
So a + B = 2003-1 = 2002
These numbers are either odd or even, so c + D = 2003
So (A-C) + (B-D)
=A-C+B-D
=(A+B)-(C+D)
=2002-2003
=-1

An isosceles triangle has a circumference of 24 cm. The ratio of the bottom to the waist is 2:3. What are the lengths of the bottom and the waist?

2:3:3
2+3+3=8
24/8=3
Bottom edge = 3x2 = 6
Waist = 3x3 = 9

As shown in the figure, point O is on the bisector of ∠ APB, and ⊙ O and PA are tangent to point C. (1) prove that the line Pb is tangent to ⊙ o; (2) the extension line of Po intersects with ⊙ o at point E. if the radius of ⊙ o is 3, PC = 4. Find the length of chord CE

(1) It is proved that: connect OC, make OD ⊥ Pb at point D. ∵ O and PA are tangent at point C, ∵ OC ⊥ pa. ∵ o is on the bisector of ∠ APB, OC ⊥ PA, OD ⊥ Pb, ∵ od = OC. ∵ linear Pb is tangent to ⊙ o; (2) let Po intersect ⊙ o at F, connect CF. ∵ OC = 3, PC = 4, ∵ Po = 5, PE = 8. ∵ o is tangent to pa

As shown in the picture, a and B are located on both sides of the river (assuming that the two sides are straight and parallel). Now a bridge is built on the river perpendicular to the river bank. How to select the location of the bridge to make the shortest distance from a to B?
[label: both banks, vertical river bank] as shown in the figure, a and B are located on both banks of the river (assuming that both banks are straight and parallel). Now, a bridge is built on the river perpendicular to the river bank. How to select the location of the bridge to make the shortest distance from a to B?

Make the vertical lines of a and B about the river bank, intersect both sides of the river bank at C and D respectively, and connect CD. Take the midpoint Q of CD and cross Q to make the vertical line about the river bank, then this vertical line is the bridge

The OD is the bisector of AOC, and the degree of BOD is calculated

There are two cases: 1. When OA is in the angle BOC, because ob is perpendicular to OC, the angle BOC = 90 degrees, because the angle BOC = angle AOC + angle AOB, because the angle AOB = 28 degrees, the angle AOC = 62 degrees, because od is the bisector of the angle AOC, the angle AOD = 1 / 2, the angle AOC, the angle AOD = 31 degrees, because the angle BOD = angle AOD + angle AOB, the angle BOD = 59 degrees 2